Question

without actual dividion, 27/125 has terminating decimal representation?​

Answer 1

Answer:

ans::

Step-by-step explanation:

yes it has terminating decimal representation

Answer 2

Yes 27/125 has terminating decimal representation. It will terminate after 3 decimal places

Given :

The fraction 27/125

To find :

without actual division , 27/125 has terminating decimal representation

Concept :

$\displaystyle\sf{Fraction = \frac{Numerator}{Denominator} }$

A fraction is said to be terminating if prime factorisation of the denominator contains only prime factors 2 and 5

If the denominator is of the form

$\sf{Denominator = {2}^{m} \times {5}^{n} }$

Then the fraction terminates after N decimal places

Where N = max { m , n }

Solution :

Step 1 of 3 :

Write down the given fraction

The given fraction is

$\displaystyle \sf{ \frac{27}{ 125 } }$

Step 2 of 3 :

Simplify the given fraction

$\displaystyle \sf{ \frac{27}{ 125 } }$

$\displaystyle \sf{ = \frac{27}{ {5}^{3} } }$

Step 3 of 3 :

Check the fraction has terminating decimal representation or not

Numerator = 27

Denominator = 5³

Since the prime factorisation of the denominator contains only prime factors as 5

So the given fraction is terminating

Since the exponent of 5 = 3

Hence the given fraction will terminate after 3 decimal places

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